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Search: id:A089395
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| A089395 |
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Prime productive numbers n: Let the digits of n be abcd. Then the numbers bcd*a+1, cd*ab+1, d*abc+1, abcd+1 etc. are all primes. If n is a k-digit number it produces k such primes. |
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4
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| 1, 2, 4, 6, 12, 16, 22, 28, 36, 52, 58, 66, 82, 106, 112, 136, 166, 178, 256, 306, 336, 352, 448, 502, 508, 556, 562, 586, 616, 652, 658, 718, 982, 1018, 1108, 1162, 1192, 1228, 1498, 1708, 2002, 2026, 2086, 2686, 2776, 2998, 3136, 3412, 3526, 3592, 4078, 4918
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Conjecture: Sequence is infinite.
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EXAMPLE
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256 is a member as 2*56 +1 = 113, 25*6 +1 = 151 and 256+1 = 257 are all primes.
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MAPLE
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with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1), j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1, op(i), d+1], i=[[], seq([j], j=2..d)])]: for n from 10^(d-1) to 10^d-1 do sn:=convert(n, base, 10): fl:=0: for s in sch do m:=mul(j, j=[seq(ds(sn[s[i]..s[i+1]-1]), i=1..nops(s)-1)])+1: if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ", n) fi od od: (C. Ronaldo)
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CROSSREFS
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Cf. A089392, A089393, A089394, A089396, A089397.
Adjacent sequences: A089392 A089393 A089394 this_sequence A089396 A089397 A089398
Sequence in context: A019280 A090748 A032465 this_sequence A089699 A089696 A099316
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 10 2003
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EXTENSIONS
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Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004
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